Abstract
The degenerate four-wave mixer is a nonlinear optical device capable of being configured to provide an extraordinarily broad range of photon statistics. The authors examine these statistics at its output in terms of the matrix representation of the process, which belongs to the SU(1,1) group of second-order unimodular matrices. The connection between this group and that of proper Lorentz transformations in two space dimensions and one time dimension permits the field density operators at the input and output ports of the device to be related by means of unitary transformations. This, in turn, provides the joint output photon number distribution for any joint input state.